论文标题
弹性的指法在旋转的Hele-Shaw细胞中
Elastic fingering in a rotating Hele-Shaw cell
论文作者
论文摘要
我们考虑弹性膜的稳态指法不稳定性，该膜在旋转的Hele-Shaw细胞中的外部压力下分离了两种不同密度的流体。都考虑了不可延迟和高度延伸的膜，并且在每种情况下都详细介绍了膜张力的作用。当内部流体的密度超过外部流体的密度时，这两个系统都表现出一个离心驱动的雷利 - 泰勒 - 泰勒的不稳定，并且这种不稳定性与曲率和张力引起的恢复力竞争，从而设定了手指尺度。数值延续不仅用于计算强烈的非线性初级手指状态，直到自我接触点，还可以计算混合模式的次级分支和圆周局部折叠，这是旋转速率和外部施加的压力的函数。计算反射对称和对称性的手性态。结果以分叉图的形式表示。发现系统尺度与自然长度尺度的比率确定了从未干扰的圆形状态以及溶液曲线和二次分叉的开始的初级分叉的排序。
We consider the steady-state fingering instability of an elastic membrane separating two fluids of different density under external pressure in a rotating Hele-Shaw cell. Both inextensible and highly extensible membranes are considered, and the role of membrane tension is detailed in each case. Both systems exhibit a centrifugally-driven Rayleigh-Taylor--like instability when the density of the inner fluid exceeds that of the outer one, and this instability competes with the restoring forces arising from curvature and tension, thereby setting the finger scale. Numerical continuation is used to compute not only strongly nonlinear primary finger states up to the point of self-contact but also secondary branches of mixed modes and circumferentially localized folds as a function of the rotation rate and the externally imposed pressure. Both reflection-symmetric and symmetry-broken chiral states are computed. The results are presented in the form of bifurcation diagrams. The ratio of system scale to the natural length scale is found to determine the ordering of the primary bifurcations from the unperturbed circle state as well as the solution profiles and onset of secondary bifurcations.
